A New Trust Region Method With MA Model

The method of moving asymptotes (MA) with trust region technique is a kind of new optimization method for solving general nonlinear programming problems, especially for structure optimization problem in engineering. The MA model is strict convex and separable, and the algorithm based on this model is globally convergent. In this paper the characters of MA model and the trust region method are analyzed, a subproblem with MA model and trust region technique is presented, and a projected gradient method is used to solve the subproblem. Based on these results we proposed a new trust region method with MA model for solving nonlinear programming problems. We discuss how to design the MA model and its parameters in this method and prove the global convergence of this method. In addition, we carry out some numerical tests for this method. It can be concluded from these results that the trust region method with MA model is efficient.In Chapter one, basic theories of optimization method and MA model are introduced. The backgrounds of nonlinear programming, trust-region method as well as projected gradient method are illustrated in the following chapter. Then it also gives the general ideas of methods for solving MA model with projected gradient method. In Chapter three, a new projected gradient method for solving MA model is given. It can deal with general nonlinear programming with trust region technique. The important properties of the improved model are analyzed and the algorithm is proposed, too. After that a MA model with trust region technique is obtained and the local convergence is proved in Chapter four, and a new trust region method is proposed for solving nonlinear programming problems. At last in Chapter five the global convergence of this method is proved. In addition, some numerical tests are given, which shows that this method is efficient.